A phase-field model for the isothermal solidification process of a binary alloy

• Autorzy: Kessler D. , Krüger O. , Rappaz J.
• Języki publikacji: EN

Abstrakty

EN

We study a phase-field model for the isothermal solidification of a binary alloy which involves the relative concentration and the order parameter. We prove the existence of weak solutions as well as regularity and uniqueness results under Lipschitz and boundeness assumptions for the nonlinearities. A maximum principle holds that justifies these assumptions. A numerical approximation and some numerical results are also presented

Słowa kluczowe

EN

isothermal solidification; binary alloy

PL

krzepnięcie izotermiczne; stop podwójny

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2000
• Tom: Vol. 7, No. 3
• Strony: 279--288
• Opis fizyczny: Bibliogr. 12 poz. rys., wykr.

Twórcy

autor

Kessler D.

• Swiss Federal Institute of Technology, EPFL, Department of Mathematics, CH-1015 Lausanne

autor

Krüger O.

• Swiss Federal Institute of Technology, EPFL, Department of Mathematics, CH-1015 Lausanne

autor

Rappaz J.

• Swiss Federal Institute of Technology, EPFL, Department of Mathematics, CH-1015 Lausanne

Bibliografia

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• [2] G. Caginalp. An analysis of a phase-field model for free boundary, Arch. Rational Mech. Anal., 92: 205-245, 1986.
• [3] J. W. Cahn, J. E. Hilliard. Free energy of a uniform system. I. Interfacial free energy, J. Chem. Phys., 28(2): 258-267, 1958.
• [4] D. Kessler. Sharp-interface limits of a thermodynamically consistent solutal phase-field model, in preparation.
• [5] D. Kessler, O. Kriiger, J. F. Scheid. Construction d'un modle de champ-de-phase temp6rature homog6ne pour la solidification d'un alliage binaire. Internal report DMA-EPFL, 1998.
• [6] D. Kessler, J. F. Scheid. An error estimate of a finite element method for a isothermal phase-field model for solidification of binary alloy, in preparation.
• [7] 0. Kriiger. Modglisation et analyse num6rique de problćmes de r6action-diffusion provenant de la solidification d'alliages binaires, PhD Thesis. EPFL 1999.
• [8] 0. Penrose, P.C. Fife. Thermodynamically consistent models of phase-field type for the kinetics of phase transitions. Physica D, 43: 44-62, 1990.
• [9] J. Rappaz, J.F. Scheid. Existence of solutions to a phase-field model for the isothermal solidification process of a binary alloy, to appear in Math. Methods Appl. Sci.
• [10] A. Visintin. Models of phase transitions, PNLDE 28, Birkhaiiser, 1996.
• [11] J. A. Warren, W. J. Boettinger. Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field model, Acta metali. mater., 43(2): 689-703 (1995).
• [12] A. A. Wheeler, W. J. Boettinger, G. B. McFadden. Phase-field model for isothermal phase transitions in binary alloys, Phys. Rev. A, 45(10): 7424-7439 (1992).